Two stage coding method

ABSTRACT

PCT No. PCT/JP85/00694 Sec. 371 Date Aug. 20, 1986 Sec. 102(e) Date Aug. 20, 1986 PCT Filed Dec. 19, 1985 PCT Pub. No. WO86/03911 PCT Pub. Date Jul. 3, 1986.Errors which arise in recording and reproducing data in a recording material are corrected with the use of an error correction code such as an RS (Reed-Solomon) code, and a two stage C2 and C1 coding method is conducted at an interval of repetition of a combination of [k2/n2] and [k2/n2]+1 on digital data having a two dimensional arrangement of k1 in the first direction and k2 in the second direction, whereby burst error correction ability is enhanced by the enhancement of error correction capacity.

TECHNICAL FIELD

The present invention relates to a two stage coding method having a highburst error correction ability and also a random error correctionability equivalent to that of the prior art when an error correctioncode such as a Reed Solomon code (hereinafter referred to as "RS code")is used in order to correct data errors which arise in reproducing datarecorded in a recording material such as a magnetic disk.

BACKGROUND ART

Generally, in recording and reproducing data into and from a recordingmaterial such as a magnetic disk a data error may arise dependent on thestate of the recording material. A data error may be a burst errorcaused by a signal drop out on a random error caused by a deteriorationin SN ratio. In order to correct these errors a two stage coded errorcorrection code is used. As an example, a two stage code using RS codeson a GF (2⁸) where q=8 will be considered. A two stage encoder is shownin FIG. 3. In FIG. 3, reference numeral 1 designates an input terminal,reference numeral 2 designates a C₂ encoder, reference numeral 3designates an interleaving circuit, reference numeral 4 designates a C₁encoder, the reference numeral 5 designates an output terminal. First ofall, C₂ encoding is performed on the original data, interleaving isexecuted thereto, and thereafter C₁ encoding is conducted, and theresulting code signal is output to the output terminal. A two stagedecoder is shown in FIG. 4. In FIG. 4, reference numeral 6 designates aninput terminal, reference numeral 7 designates a C₁ decoder, referencenumeral 8 designates a deinterleaving circuit, reference numeral 9designates a C₂ decoder, and reference numeral 10 designates an outputterminal. In this decoder deinterleaving is executed after the C₁decoding, and thereafter C₂ decoding is conducted. There is a prior arttwo stage coding method which, assuming that data obtained by arrangingk₁ ×9 digits in a first direction and k₂ digits (k₁ <k₂) in a seconddirection as shown in FIG. 5 is arranged into 8 data words in the firstdirection, consists of adding a first check code of n₂ -k₁ digits, andthereafter adding a second check code of n₁ -n₂ digits as shown in FIG.2. (n₂, k₁) RS code is used as the C₂ code, and (n₁, n₂) RS code is usedas the C₁ code.

A specific coding example will be described with reference to FIGS. 5and 2. When it is established that k₁ =32, k₂ =128, n₁ =40, n₂ =36, andh₁ =h₂ =. . . =h₃₅ =h=3, the data region comprising the data and thefirst check code becomes data of n₂ ×k₂ =4608 digits as shown in FIG. 5,and when a₁ is set to 1, a₂ to a₃₆ become as follows: ##EQU1## and C₂encoding is conducted on the data corresponding to the a₁ -th, a₂ -th, .. . , a₃₂ -th data with the use of the following generation polynomialof C₂ code ##EQU2## where α is a root of a primary polynomial (forexample, such as x⁸ +x⁴ +x³ +x² +1 on GF (2⁸)). The generated checkcodes are arranged at the positions corresponding to the a₃₃ -th, a₃₄-th, . . . , a₃₆ -th data. Next, a₁ is set as follows:

    a.sub.1 =a.sub.1 +n.sub.2 =a.sub.1 +36,

and similarly check codes are added to the data successively. Herein, ifthe calculated result of a₂ to a₃₆ exceeds n₂ ×k₂ =4608, a numberobtained by subtracting 4608 therefrom is made the result. The encodingis repeated k₂ times thereby to conclude the C₂ encoding.

Next, C₁ encoding is conducted on the data of n₂ digits in each columnarranged in the first direction as shown in FIG. 2 with the use of thefollowing generation polynomial of C₁ code ##EQU3## The generated checkcode is added to the end portion of the data and the encoding isrepeated k₂ times. In the recording of the data onto the recordingmaterial data of n₁ =40 digits arranged in the first direction is sentout k₂ times successively. In the reproduction of the same the sent outdata are arranged in a column in the first direction by 40 digitssuccessively.

In the prior art two stage coding method with such a construction, theC₂ code is concerned with burst error correction ability, and the C₁ andC₂ codes are concerned with random error correction ability. In thestage of conducting C₂ encoding the h must be made large in order toenhance the burst error correction ability, and h is set as follows:

    h=[k.sub.2 /n.sub.2]=[ 128/36]=3

The C₂ codes are gathered at the right end portion of the data region inFIG. 5, and the C₂ and the C₁ code are arranged adjacent to each otherin the first direction subsequent to the data of k₁ =32 digits when theC₁ encoding is completed.

The prior art two stage coding method is constructed in such a manner,and the error correction ability by one code amounts to n₂ -k₁ digitswhen forfeiture correction is conducted by the C₂ decoding. Accordingly,the burst error correction ability becomes as follows for data of n₂ ×k₂=4608 digits comprising all the data and the C₂ code

    (n.sub.2 -k.sub.1)×n.sub.2 ×h=432,

but h becomes as follows:

    h=[k.sub.2 /n.sub.2 ]=[128/36]=3<128/36,

and k₂ /n₂ does not equal an integer, thereby resulting in deteriorationof error correction capability.

DISCLOSURE OF THE INVENTION

The present invention is directed to solve the problems pointed outabove and an object is to provide a two stage coding method in which theabove-described deterioration in a burst error correction ability isimproved and a higher burst error correction ability than that of theprior art device is obtained.

According to the coding method of the present invention, assuming thatdata of k₁ ×8×k₂ digits are arranged in a matrix of k₁ ×8 digits in afirst direction and k₂ digits(s) in a second direction and the data isdivided into words of 8 digit(s) in the first direction, in conductingC₂ encoding by taking out n₂ data words from the data of n₂ words in thefirst direction and k₂ words in the second direction with no duplicationof data in either of the first and second directions, a C₂ code of codelength n₂ is produced by establishing a₁ at an arbitrary data numberword, and establishing h₁, h₂, . . . , h_(n2-1) such that they become arepetition of a combination satisfying the condition that [k₂ /n₂ ] and[k₂ /n₂ ]+1 may be

    [k.sub.2 /n.sub.2 ]×1.sub.1 +([k.sub.2 /n.sub.2 ]+1)×1.sub.2 ≦k.sub.2

(herein, 1₁ +1₂ =n₂ (1₁, 1₂ : integer) and a₂ to a_(n2) exceeding n₂ ×k₂are obtained by subtracting n₂ ×k₂ therefrom) for a₂ to a_(n2) as in thefollowing:

    a.sub.2 =a.sub.1 +n.sub.2 ×h1+1 ##EQU4## when numbering is conducted successively in the first direction on the data of n.sub.2 words in the first direction and k.sub.2 words in the second direction, and this is repeated k.sub.2 times in the second direction, and thereafter C.sub.1 encoding of each n.sub.2 ×q digits in the first direction into a code length n.sub.1 is conducted.

In the two stage coding method of the present invention, C₂ codes areconstructed to be effective for error correction at the portion of n₂-k₁ in the first direction and at the portion of k₂ in the seconddirection against the data obtained by arranging k₁ digits in the firstdirection and k₂ digits in the second direction, as shown in FIG. 1.Accoding to the present invention, the burst error correction abilityagainst the data of n₂ ×k₂ =4608 digits comprising all the data, and theC₂ codes becomes

    (n.sub.2 -k.sub.1)×n.sub.2 ×(h.sub.A +h.sub.B)/2=504,

and this exceeds 432 which is the burst error correction ability of theprior art device against the same number of data and the same number ofcheck codes.

In this way, it is possible to conduct a two stage coding having ahigher burst error correction ability than that of the prior art, andhaving a random error correction ability equivalent to that of the priorart due to the C₁ and C₂ codes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a data arrangement for conducting a C₂encoding method as one embodiment of the present invention;

FIG. 2 is a diagram showing a data arrangement for conducting a priorart two stage coding method and a C₁ encoding method as an embodiment ofthe present invention;

FIG. 3 is a block diagram showing a two stage encoding circuit;

FIG. 4 is a block diagram showing a two stage decoding circuit; and

FIG. 5 is a diagram showing a data arrangement for conducting the C₂encoding method of the prior art two stage coding method.

BEST MODES OF EMBODYING THE INVENTION

Embodiments of the present invention will be described with reference tothe drawings. In FIGS. 1 and 2, the constants are established that q=8,k₁ =32, k₂ =128, n₁ =40, n₂ =36, and data are divided into words of 8digits in the first direction. FIG. 1 shows a C₂ encoding method. Dataof k₁ ×k₂ =4096 data words are arranged sequentially in the firstdirection and in a matrix of k₁ =32 words in the first direction and k₂=128 words in the second direction, and when h_(2i-1) and h_(2i) are setas follows

    h.sub.2i-1 =h.sub.A =[k.sub.2 /n.sub.2 ]=3

    h.sub.2i =h.sub.B =[k.sub.2 /n.sub.2 ]+1=4,

(i: integer, 1≦i≦(n₂ -1)/2)

and a₁ is set 1, a₂ to a₃₆ become ##EQU5## and, C₂ encoding is performedon the data corresponding to the a₁ -th, a₂ -th, . . . , and a₃₂ -thdata with the use of the generation polynomial of the C₂ code ##EQU6##Herein, α is a root of a primary polynomial. The generated check codesare arranged at the positions corresponding to the a₃₃ -th, a₃₄ -th, . .. , a₃₆ -th data. Next, a₁ is set as follows

    a.sub.1 =a.sub.1 +n.sub.2 =a.sub.1 +36

and similarly inspection codes are added to the data successively. a₂ toa₃₆ exceeding n₂ ×k₂ =4608 are made by subtracting 4608 therefrom. Whenthis encoding operation is repeated k₂ times the C₂ encoding iscompleted.

Next, C₁ encoding is performed on the data of n₂ words in each columnarranged in the first direction as shown in FIG. 2 with the use of thegeneration polynomial of C₁ code ##EQU7## The generated check codes areadded to the data, and the encoding is repeated k₂ times. The recordingof the data on a recording material is conducted by sending out data ofn₁ =40 words arranged in the first direction successively k₂ times. Thedata format reproduction is conducted by arranging the sent out data by40 words successively in a column in the first direction.

In the two stage coding method of the present invention, the C₂ code isconcerned with burst error correction ability and both C₁ and C₂ codesare concerned with random error correction ability. In conducting the C₂encoding, C₂ codes of n₂ -k₁ in the first direction and k₂ in the seconddirection can be used effectively for the error correction of the dataarranged in a matrix of k₁ in the first direction and k₂ in the seconddirection.

In the above-illustrated embodiment a repetition pattern of (h_(A),h_(B)) is adopted for h₁, h₂, . . . , h_(n2-1), but other combinationsusing h_(A) and h_(B) such as (h_(B), h_(A)) or (h_(A), h_(B), h_(B))can be used if they comply with the following conditions

    h.sub.A ×l.sub.1 +h.sub.B ×l.sub.2 ≦k.sub.2

    l.sub.1 +l.sub.2 =n.sub.2

Furthermore, an RS code on GF (2^(q)) is used as an error correctioncode, but another code such as a BCH code can be used as an errorcorrection code. Furthermore, the number of data, the construction ofinformation lengths in the first and second directions, and the C₂ andC₁ code lengths can be arbitrarily established. Furthermore, in theillustrated embodiment the region occupied by the check codes of the C₂code and the C₁ code is shown in FIG. 2, but this occupied region can bearbitrarily established by establishing a₁ at an arbitrary number.

Furthermore, it is possible to add the additional information of k₃ ×qdigits in the second direction k₂ times precedent to the C₁ encoding,and thereafter to conduct C₁ encoding on GF (2^(q)) having the (n₁+k₃)×q digits in the first direction, and to conduct a coding k₂ timesrepeatedly in the second direction.

APPLICABILITY TO THE INDUSTRY

The present invention is applicable not only to a magnetic diskapparatus but also to an optical recording and reproducing apparatus,and an optical magnetic recording and reproducing apparatus.

We claim:
 1. A two stage coding system for encoding digital informationarranged in a matrix of k₁ ×q digits in a first direction, and k₂ digitsin a second direction orthogonal to the first direction, whereinK₁, q,and k₂ are integers, K₁ <k₂ ; q=the number of digits per data word, andK₁, K₂ =the number of data words in said first and second directionsrespectively, comprising: C₂ encoder means for encoding said digitalinformation with a C₂ code on a Galois Field GF (2^(q)), including meansfor numbering data words in said matrix diagonally from an arbitrarydata word a₁ and establishing a₂ to a_(n2), wherein n₂ is the length ofcode C₂, such that ##EQU8## wherein h₁ to h_(n).sbsb.2.spsb.-1 satisfythe following

    h.sub.2i-1 =[K.sub.2 /n.sub.2 ]

    h.sub.2i =[k.sub.2 /n.sub.2 ]+1 1≦i≦(n.sub.2 -1)/2

means for C₂ encoding said numbered data words, and means for adding theobtained C₂ code to an end of said matrix in said first direction; andC₁ encoder means for encoding said C₂ encoded matrix with a C₁ codehaving a length of n₁ on a GF (2^(q)) for each row of data words in saidfirst direction, and adding the obtained C₁ code to an end of saidmatrix in said first direction.